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<H3>fix wall/lj93 command 
</H3>
<H3>fix wall/lj126 command 
</H3>
<H3>fix wall/colloid command 
</H3>
<H3>fix wall/harmonic command 
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID style face args ... keyword value ... 
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command 

<LI>style = <I>wall/lj93</I> or <I>wall/lj126</I> or <I>wall/colloid</I> or <I>wall/harmonic</I> 

<LI>one or more face/arg pairs may be appended 

<LI>face = <I>xlo</I> or <I>xhi</I> or <I>ylo</I> or <I>yhi</I> or <I>zlo</I> or <I>zhi</I> 

<PRE>  args = coord epsilon sigma cutoff
    coord = position of wall = EDGE or constant or variable
      EDGE = current lo or hi edge of simulation box
      constant = number like 0.0 or -30.0 (distance units)
      variable = <A HREF = "variable.html">equal-style variable</A> like v_x or v_wiggle
    epsilon = strength factor for wall-particle interaction (energy or energy/distance^2 units)
      epsilon can be a variable (see below)
    sigma = size factor for wall-particle interaction (distance units)
      sigma can be a variable (see below)
    cutoff = distance from wall at which wall-particle interaction is cut off (distance units) 
</PRE>
<LI>zero or more keyword/value pairs may be appended 

<LI>keyword = <I>units</I> or <I>fld</I> 

<PRE>  <I>units</I> value = <I>lattice</I> or <I>box</I>
    <I>lattice</I> = the wall position is defined in lattice units
    <I>box</I> = the wall position is defined in simulation box units
  <I>fld</I> value = <I>yes</I> or <I>no</I>
    <I>yes</I> = invoke the wall constraint to be compatible with implicit FLD
    <I>no</I> = invoke the wall constraint in the normal way
  <I>pbc</I> value = <I>yes</I> or <I>no</I>
    <I>yes</I> = allow periodic boundary in a wall dimension
    <I>no</I> = require non-perioidic boundaries in any wall dimension 
</PRE>

</UL>
<P><B>Examples:</B>
</P>
<PRE>fix wallhi all wall/lj93 xlo -1.0 1.0 1.0 2.5 units box
fix wallhi all wall/lj93 xhi EDGE 1.0 1.0 2.5
fix wallhi all wall/lj126 v_wiggle 23.2 1.0 1.0 2.5
fix zwalls all wall/colloid zlo 0.0 1.0 1.0 0.858 zhi 40.0 1.0 1.0 0.858 
</PRE>
<P><B>Description:</B>
</P>
<P>Bound the simulation domain on one or more of its faces with a flat
wall that interacts with the atoms in the group by generating a force
on the atom in a direction perpendicular to the wall.  The energy of
wall-particle interactions depends on the style.
</P>
<P>For style <I>wall/lj93</I>, the energy E is given by the 9/3 potential:
</P>
<CENTER><IMG SRC = "Eqs/fix_wall_lj93.jpg">
</CENTER>
<P>For style <I>wall/lj126</I>, the energy E is given by the 12/6 potential:
</P>
<CENTER><IMG SRC = "Eqs/pair_lj.jpg">
</CENTER>
<P>For style <I>wall/colloid</I>, the energy E is given by an integrated form
of the <A HREF = "pair_colloid.html">pair_style colloid</A> potential:
</P>
<CENTER><IMG SRC = "Eqs/fix_wall_colloid.jpg">
</CENTER>
<P>For style <I>wall/harmonic</I>, the energy E is given by a harmonic spring
potential:
</P>
<CENTER><IMG SRC = "Eqs/fix_wall_harmonic.jpg">
</CENTER>
<P>In all cases, <I>r</I> is the distance from the particle to the wall at
position <I>coord</I>, and Rc is the <I>cutoff</I> distance at which the
particle and wall no longer interact.  The energy of the wall
potential is shifted so that the wall-particle interaction energy is
0.0 at the cutoff distance.
</P>
<P>Up to 6 walls or faces can be specified in a single command: <I>xlo</I>,
<I>xhi</I>, <I>ylo</I>, <I>yhi</I>, <I>zlo</I>, <I>zhi</I>.  A <I>lo</I> face interacts with
particles near the lower side of the simulation box in that dimension.
A <I>hi</I> face interacts with particles near the upper side of the
simulation box in that dimension.
</P>
<P>The position of each wall can be specified in one of 3 ways: as the
EDGE of the simulation box, as a constant value, or as a variable.  If
EDGE is used, then the corresponding boundary of the current
simulation box is used.  If a numeric constant is specified then the
wall is placed at that position in the appropriate dimension (x, y, or
z).  In both the EDGE and constant cases, the wall will never move.
If the wall position is a variable, it should be specified as v_name,
where name is an <A HREF = "variable.html">equal-style variable</A> name.  In this
case the variable is evaluated each timestep and the result becomes
the current position of the reflecting wall.  Equal-style variables
can specify formulas with various mathematical functions, and include
<A HREF = "thermo_style.html">thermo_style</A> command keywords for the simulation
box parameters and timestep and elapsed time.  Thus it is easy to
specify a time-dependent wall position.  See examples below.
</P>
<P>For the <I>wall/lj93</I> and <I>wall/lj126</I> styles, <I>epsilon</I> and <I>sigma</I> are
the usual Lennard-Jones parameters, which determine the strength and
size of the particle as it interacts with the wall.  Epsilon has
energy units.  Note that this <I>epsilon</I> and <I>sigma</I> may be different
than any <I>epsilon</I> or <I>sigma</I> values defined for a pair style that
computes particle-particle interactions.
</P>
<P>The <I>wall/lj93</I> interaction is derived by integrating over a 3d
half-lattice of Lennard-Jones 12/6 particles.  The <I>wall/lj126</I>
interaction is effectively a harder, more repulsive wall interaction.
</P>
<P>For the <I>wall/colloid</I> style, <I>R</I> is the radius of the colloid
particle, <I>D</I> is the distance from the surface of the colloid particle
to the wall (r-R), and <I>sigma</I> is the size of a constituent LJ
particle inside the colloid particle and wall.  Note that the cutoff
distance Rc in this case is the distance from the colloid particle
center to the wall.  The prefactor <I>epsilon</I> can be thought of as an
effective Hamaker constant with energy units for the strength of the
colloid-wall interaction.  More specifically, the <I>epsilon</I> pre-factor
= 4 * pi^2 * rho_wall * rho_colloid * epsilon * sigma^6, where epsilon
and sigma are the LJ parameters for the constituent LJ
particles. Rho_wall and rho_colloid are the number density of the
constituent particles, in the wall and colloid respectively, in units
of 1/volume.
</P>
<P>The <I>wall/colloid</I> interaction is derived by integrating over
constituent LJ particles of size <I>sigma</I> within the colloid particle
and a 3d half-lattice of Lennard-Jones 12/6 particles of size <I>sigma</I>
in the wall.  As mentioned in the preceeding paragraph, the density of
particles in the wall and colloid can be different, as specified by
the <I>epsilon</I> pre-factor.
</P>
<P>For the <I>wall/harmonic</I> style, <I>epsilon</I> is effectively the spring
constant K, and has units (energy/distance^2).  The input parameter
<I>sigma</I> is ignored.  The minimum energy position of the harmonic
spring is at the <I>cutoff</I>.  This is a repulsive-only spring since the
interaction is truncated at the <I>cutoff</I>
</P>
<P>For any wall, the <I>epsilon</I> and/or <I>sigma</I> parameter can be specified
as an <A HREF = "variable.html">equal-style variable</A>, in which case it should be
specified as v_name, where name is the variable name.  As with a
variable wall position, the variable is evaluated each timestep and
the result becomes the current epsilon or sigma of the wall.
Equal-style variables can specify formulas with various mathematical
functions, and include <A HREF = "thermo_style.html">thermo_style</A> command
keywords for the simulation box parameters and timestep and elapsed
time.  Thus it is easy to specify a time-dependent wall interaction.
</P>
<P>IMPORTANT NOTE: For all of the styles, you must insure that r is
always > 0 for all particles in the group, or LAMMPS will generate an
error.  This means you cannot start your simulation with particles at
the wall position <I>coord</I> (r = 0) or with particles on the wrong side
of the wall (r < 0).  For the <I>wall/lj93</I> and <I>wall/lj126</I> styles, the
energy of the wall/particle interaction (and hence the force on the
particle) blows up as r -> 0.  The <I>wall/colloid</I> style is even more
restrictive, since the energy blows up as D = r-R -> 0.  This means
the finite-size particles of radius R must be a distance larger than R
from the wall position <I>coord</I>.  The <I>harmonic</I> style is a softer
potential and does not blow up as r -> 0, but you must use a large
enough <I>epsilon</I> that particles always reamin on the correct side of
the wall (r > 0).
</P>
<P>The <I>units</I> keyword determines the meaning of the distance units used
to define a wall position, but only when a numeric constant or
variable is used.  It is not relevant when EDGE is used to specify a
face position.  In the variable case, the variable is assumed to
produce a value compatible with the <I>units</I> setting you specify.
</P>
<P>A <I>box</I> value selects standard distance units as defined by the
<A HREF = "units.html">units</A> command, e.g. Angstroms for units = real or metal.
A <I>lattice</I> value means the distance units are in lattice spacings.
The <A HREF = "lattice.html">lattice</A> command must have been previously used to
define the lattice spacings.
</P>
<P>The <I>fld</I> keyword can be used with a <I>yes</I> setting to invoke the wall
constraint before pairwise interactions are computed.  This allows an
implicit FLD model using <A HREF = "pair_lubricateU.html">pair_style lubricateU</A>
to include the wall force in its calculations.  If the setting is
<I>no</I>, wall forces are imposed after pairwise interactions, in the
usual manner.
</P>
<P>The <I>pbc</I> keyword can be used with a <I>yes</I> setting to allow walls to
be specified in a periodic dimension.  See the
<A HREF = "boundary.html">boundary</A> command for options on simulation box
boundaries.  The default for <I>pbc</I> is <I>no</I>, which means the system
must be non-periodic when using a wall.  But you may wish to use a
periodic box.  E.g. to allow some particles to interact with the wall
via the fix group-ID, and others to pass through it and wrap around a
periodic box.  In this case you should insure that the wall if
sufficiently far enough away from the box boundary.  If you do not,
then particles may interact with both the wall and with periodic
images on the other side of the box, which is probably not what you
want.
</P>
<HR>

<P>Here are examples of variable definitions that move the wall position
in a time-dependent fashion using equal-style
<A HREF = "variable.html">variables</A>.  The wall interaction parameters (epsilon,
sigma) could be varied with additional variable definitions.
</P>
<PRE>variable ramp equal ramp(0,10)
fix 1 all wall xlo v_ramp 1.0 1.0 2.5 
</PRE>
<PRE>variable linear equal vdisplace(0,20)
fix 1 all wall xlo v_linear 1.0 1.0 2.5 
</PRE>
<PRE>variable wiggle equal swiggle(0.0,5.0,3.0)
fix 1 all wall xlo v_wiggle 1.0 1.0 2.5 
</PRE>
<PRE>variable wiggle equal cwiggle(0.0,5.0,3.0)
fix 1 all wall xlo v_wiggle 1.0 1.0 2.5 
</PRE>
<P>The ramp(lo,hi) function adjusts the wall position linearly from lo to
hi over the course of a run.  The vdisplace(c0,velocity) function does
something similar using the equation position = c0 + velocity*delta,
where delta is the elapsed time.
</P>
<P>The swiggle(c0,A,period) function causes the wall position to
oscillate sinusoidally according to this equation, where omega = 2 PI
/ period:
</P>
<PRE>position = c0 + A sin(omega*delta) 
</PRE>
<P>The cwiggle(c0,A,period) function causes the wall position to
oscillate sinusoidally according to this equation, which will have an
initial wall velocity of 0.0, and thus may impose a gentler
perturbation on the particles:
</P>
<PRE>position = c0 + A (1 - cos(omega*delta)) 
</PRE>
<HR>

<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
</P>
<P>No information about this fix is written to <A HREF = "restart.html">binary restart
files</A>.
</P>
<P>The <A HREF = "fix_modify.html">fix_modify</A> <I>energy</I> option is supported by this
fix to add the energy of interaction between atoms and each wall to
the system's potential energy as part of <A HREF = "thermo_style.html">thermodynamic
output</A>.
</P>
<P>This fix computes a global scalar energy and a global vector of
forces, which can be accessed by various <A HREF = "Section_howto.html#howto_15">output
commands</A>.  Note that the scalar energy is
the sum of interactions with all defined walls.  If you want the
energy on a per-wall basis, you need to use multiple fix wall
commands.  The length of the vector is equal to the number of walls
defined by the fix.  Each vector value is the normal force on a
specific wall.  Note that an outward force on a wall will be a
negative value for <I>lo</I> walls and a positive value for <I>hi</I> walls.
The scalar and vector values calculated by this fix are "extensive".
</P>
<P>No parameter of this fix can be used with the <I>start/stop</I> keywords of
the <A HREF = "run.html">run</A> command.
</P>
<P>The forces due to this fix are imposed during an energy minimization,
invoked by the <A HREF = "minimize.html">minimize</A> command.
</P>
<P>IMPORTANT NOTE: If you want the atom/wall interaction energy to be
included in the total potential energy of the system (the quantity
being minimized), you MUST enable the <A HREF = "fix_modify.html">fix_modify</A>
<I>energy</I> option for this fix.
</P>
<P><B>Restrictions:</B> none
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_wall_reflect.html">fix wall/reflect</A>,
<A HREF = "fix_wall_gran.html">fix wall/gran</A>,
<A HREF = "fix_wall_region.html">fix wall/region</A>
</P>
<P><B>Default:</B>
</P>
<P>The option defaults units = lattice, fld = no, and pbc = no.
</P>
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